The teacher who taught this, should be severely reprimanded and threatened with firing if she repeats this to another student.
Hashem wants you to daven. Period. He doesn’t want you to keep a counter for each perek tehillim, for each shmoneh esrei or chessed that you do. If someone is ill, daven for them, again, without a counter. As to why that person is ill, that’s the ribbono shel olams business not mine or yours.